Rotary indexing mechanism

ABSTRACT

A multiple step rotary indexing machine which is used for indexing a rotary table around an axis. A stationary reaction member such as an internal gear or a sun gear is surrounded by a plurality of planetary gears having an input shaft on one side and an output shaft on the other side. Radial slide members or links connect the input shafts to a rotary power input and similar members connect the output shafts to the rotary table such that a constant input speed can produce a suitably accelerated and decelerated output with a selected dwell period at a selected angle on the rotation.

5 A United States Patent [191 [111 mamas Brains 1 May 1, N73

[ ROTARY INDEXING MECHANISM Primary Examiner-Leonard H. Gerin [76]inventor: John Henry Brems, 32867 White Attorney-Arthur Ralsch et OaksTrail, Birmmgham, Mich. ABSTRACT F'l D 17, 1971 [22] l ed ec A multiplestep rotary indexing machine WlllCh 15 used [21] Appl. No.: 209,319 forindexing a rotary table around an axis. A stationary reaction membersuch as an internal gear or a sun gear is surrounded by a plurality ofplanetary gears ((5! having an input Shaft on one Side and an outputShaft Fieid 74/394 on the other side. Radial slide members or links conrmet the input Shafts to a rotary power input and similar members connectthe output shafts to the r0- [56] References cued tary table such that aconstant input speed can UNITED STATES PATENTS produce a suitablyaccelerated and decelerated output with a selected dwell period at aselected angle on the 3,407,678 10/1968 Steinke rotation 3,618,722 l1/1971 Eschenbach ..74/394 X 11 Claims, 24 Drawing Figures Patented May1, 1973 10 Sheets-Sheet 1 F I G l SECZ-GG F' I G 2 Patented May 1, 1973l0 Sheets-Sheet I5 FIGJO Patented May 1, 1973 3,730,014

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Pl 141%! 7192 Y Patented May 1, 1973 10 Sheets-Sheet s Patented May 1,1973 10 Sheets-Sheet 5! a w a m m b6 M 4 .0 Z w 9/ u w J: 4 a, w. m V aW 00 Y 5 3 r f a w w m 5. Z m m H/ aw m a, A 6 w w o x a r 00 1 /3 flu m.fJ I! 09 NvQbR o a z a a 5 6. 4. d 3 3 3 3 3 2 0 0 0 Patented May 1,1973 10 Sheets-Sheet LO ROTARY INDEXING MECHANISM This invention relatesto a Rotary Indexing Mechanism which generates an intermittent outputmotion having highly variable output characteristics.

In manufacturing procedures, rotary index mechanisms in a wide varietyof styles and output characteristics are employed to move parts from onework station to another where different operations are performed. Ingeneral, the output table supports a number of equally spaced worksupport fixtures which carry workpieces to the various operativemachines. Problems have developed in connection with these machines asto acceleration and deceleration, unnecessary time delays, inaccuratestopping points, lack of necessary torque at certain stages in themotion, lack of flexibility in design, inadequate locking means at theindividual stations, and absence of smooth acceleration and decelerationcharacteristics.

It is an object of this invention to provide a mechanism which, forconditions of constant input velocity, generates an output motion havingintermittent stops with smooth acceleration and deceleration betweenstops.

It is a further object of this invention to provide a rotary indexingmechanism in which the dwell at the output stopping points may be variedby controlling certain parameters.

It is a further object of this invention to provide a rotary indexingmechanism in which the output displacement, velocity, and accelerationcharacteristics may be varied over a wide range by the choice of certainparameters.

It is a further object of this invention to provide a rotary indexingmechanism which, by virtue of multiple drive points, can achieve veryhigh output torques for a given size.

It is a further object of this invention to provide a rotary indexingmechanism in which the output is inherently locked during its 'dwellposition by the inherent characteristics of the mechanism.

his a further object of this invention to provide an auxiliary precisionlocking mechanism which is actuated by the basic rotary index mechanism,thereby increasing both the accuracy of the stopping point and thelocked torque capacity.

It is a further object of this invention to provide a rotary outputmechanism in which the output member rotates through one or morerevolutions while going through its acceleration and deceleration cycle.

It is the purpose of the present invention to index an output tablethrough a fractional revolution from one stopped position to another,smoothly accelerating to a maximum speed and then smoothly acceleratingto a stop. The novel mechanism described herein is capable of achievingthis result generating a very high torque with a relatively smallmechanism due to the use of multiple drive points. Furthermore, thecharacteristics of displacement, velocity, and acceleration for an indexcycle can be varied over an extremely wide range through suitable choiceof certain internal geometric parameters. This includes such variationsas non-symmetry about the midpoint of index of the outputcharacteristics which is valuable in many applications.

The mechanism is equally useful for producing output index angles of onefull revolution, or even multiple revolutions, while still maintainingthe desired smooth acceleration and deceleration and variabilitycharacteristics. This makes it applicable to such functions as stockfeeding, peripheral indexing and linear indexing through a rack andpinion output system.

Other applications arise in which a complete stop or dwell of the outputis not required but where it is still desired to have a periodicvariation in the output velocity. Again, through choice of certaingeometric parameters, the mechanism disclosed herein is capable ofmeeting such requirements with a high degree of flexibility.

The mechanism may be built in two basic modes, a slide mode or a linkmode; and in two basic styles, external planetaries or internalplanetaries, with cross variations and sub-variations on each.

Other objects and features of the invention relating to details ofconstruction together with the principles thereof and the manner of useand operation will be apparent in the following description and claimsin which there is set forth the best mode presently contemplated forpractice of the invention.

Drawings accompany the disclosure and the various views thereof may bebriefly described as follows:

FIG. 1, a split midplane longitudinal section through one embodiment ofthe mechanism, taken respectively on lines GG and I-II-I of FIG. 2utilizing an external planetary system with a slide mode.

FIG. 2, a series of stepped sections through the mechanism of FIG. 1,taken respectively on lines B-B, CC, DD, E-E and FF of FIG. 1.

FIG. 3, a split midplane longitudinal section through a secondembodiment of the mechanism, taken respectively on lines GG and HH ofFIG. 4 utilizing an internal planetary system with a slide mode.

FIG. 4, a series of stepped section through the mechanism of FIG. 3,taken respectively on lines B-B, CC, DD, E-E and F-F ofFIG. 3.

FIG. 5, a split midplane longitudinal section through a third embodimentof the mechanism, taken on line F-F of FIG. 6 utilizing a link mode withthe internal planetaries.

FIGS. 6 to 10, a series of transverse sections through the mechanism ofFIG. 5, taken respectively on lines AA, B-B, CC, DD, and EE of FIG. 5.

FIG. 11, a split midplane longitudinal section through a fourthembodiment of the mechanism, taken on line DD of FIG. 12 showing a linkmode with external planetaries.

FIGS. 12 to 14, a series of transverse sections through the mechanism ofFIG. 11, taken respectively on lines A-A, 8-3 and CC of FIG. 11.

FIGS. l5, l6, kinematic line drawings for a slide mode, external gearsystem.

FIGS. 17, 18, kinematic line drawings for a slide mode, internal gearsystem.

FIG. 19, a series of curves showing relative angular velocities of aslide mode mechanism with external planetaries.

FIG. 20, a series of curvesshowing relative angular velocities of aslide mode mechanism with a sun gear radius of 4.

FIG. 21, a series of curves showing relative angular velocities forexternal planetaries in an out-of-phase slide mode mechanism.

FIG. 22, a series of curves showing relative angular velocities for aslide mode, in-phase system with internal planetaries.

FIG. 23, a series of curves showing relative angular velocities for aslide mode, in-phase system with internal planetaries with a radius of4.

FIG. 24, a series of curves showing relative angular velocities for anout-of-phase, slide mode, internal planetary system wherein theparameter R is 0.50 and the radius of the planetary is 4.

Referring to FIGS. -1 and 2, a case 10, consisting of an essentiallycircular weldment or casting, is the frame to which three sets ofrotating members are attached. In the specific arrangement shown, theoutput member consists of a turntable 12 attached to the case throughoutput bearing 14. The inner race of the bearing 14 is clamped to thecase 10 by clamp ring 16, while the outer race is clamped to theturntable through spacer 18 and clamp ring 20.

The turntable 12 is indirectly driven by a family of planetary gears.Six such identical planetary gears are shown in the drawings, FIGS. 1and 2, but it will be understood that this number is arbitrary and canbe increased or decreased within reasonable limits to meet the loadrequirements of the application.

On the underside of the turntable are mounted six pairs of drive bars22, section B-B, FIG. 2. Into the slot formed by each pair of thesedrive bars 22 is slidably mounted a guide block 24, which is in turnrotatably connected to an output eccentric 26, integral with or boltedto a planetary gear 28. The distance from the centerline of eacheccentric 26 to the centerline of each planetary gear 28 may vary fromdesign to design from O to slightly more than the pitch radius of theplanetary gear 28. This is later referred to as dimension R Eachplanetary gear 28 is guided by two bearings 30 and 32 mounted, FIG. 1,section GG, in a planetary carrier assembly consisting of the lower ringplate 34,

- the upper ring plate 36, and six spacers 38. The lower ring plate inturn is connected to the case 10 through bearing 40 which thereby guidesthe entire planetary carrier assembly 34, 36 and 38.

Each of the planetary gears 28 is suitably formed to mesh with astationary sun gear 42 which is rigidly bolted to the case 10. It can beseen, therefore, that when the planetary carrier assembly 34, 36 and 38is rotated on its bearing 40, through means described below, theplanetary gears 28 are caused to rotate about their individualcenterlines, as well as revolving about the sun gear 42. This in turncauses the output eccentrics 26 to drive the turntable 12 through guideblocks 24 and drive bars 22. It will be further seen that the motion ofthe turntable l2 will be of an intermittent nature depending on theeccentricity of the output eccentric 26 relative to the pitch radius ofthe planetary gear 28.

An input eccentric 44 is integral with or bolted to each planetary gear28. Each input eccentric 44 is rotatably connected to a slide block 46which is slidably mounted in a slot 48 in the input driver ring 50, FIG.2, Section F-F. This input driver ring 50 is supported from the case 10through bearing 52, which is fastened to the case 10 by clamp ring 54,and clamped to the input driver ring 50 by clamp ring 56. The

distance from the centerline of each planetary gear 28 to the centerlineof each input eccentric 44 may vary from design to design from O toslightly less than the pitch radius of the planetary gear 28. Thisdimension is later referred to as R It will be seen that as the inputdriver ring is rotated on its support bearing 52, the planetary gears 28and the planetary carrier assembly 34, 36 and 38 are driven through theslots 48, the slide blocks 46, and the input eccentrics 44. Thecharacteristics of motion of the planetary carrier assembly 34, 36 and38 relative to the driver ring 50 are determined by the amount ofeccentricity of the input eccentrics 44.

Therefore, the rotation of the driver ring 50 causes an intermittentrotation of the turntable l2, and the characteristics of the turntablel2 movement are dependent on the eccentricities of both the input andoutput eccentrics relative to the centers of the planetary gears.

In the drawings presented in FIGS. 1 and 2, the input and outputeccentrics are shown as lying in the same radial plane of each planetarygear. The output characteristics of the turntable may be furthercontrolled by introducing an angle between the radial plane thatcontains the input eccentric and the radial plane that contains theoutput eccentric. The effect of these quantities, input eccentricity,output eccentricity, and phase angle between them, will be analyzed inthe kinematic section below.

The input driver ring 50 may be driven by one of a variety ofconventional systems among which are: a worm driving against the outsidesurface of the driver ring 50 into which appropriate worm wheel teethhave been cut; a small pinion 51 on a drive shaft 51A driving againstthe outside surface of the driver ring 50 into which appropriate matinggear teeth have been cut (FIG. 2); a chain or belt drive engagingsuitable sprocket teeth or belt grooves in the driving ring 50; a

cylinder drive through a pawl and ratchet arrangement, the ratchetmember being attached to or integral with the driver ring 50; foroscillatory as opposed to unidirectional indexing, a cylinder output rodmay be directly pin connected to the driver ring 50.

In the design presented in FIGS. 1 and 2, the planetary gears were shownoperating around a stationary sun gear creating an external planetarydesign. An alternate design in which the planetary gears operate withina stationary internal gear is next described; this is referred to as aninternal planetary design.

Referring to FIGS. 3 and 4, a case 60, consisting of an essentiallycircular weldmentor casting, is the frame to which three sets ofrotating members are attached. In the specific arrangement shown, theoutput member consists of a turntable 62 attached to the case throughoutput bearing 64. The outer race of the hearing 64 is clamped to thecase 60 by clamp ring 66, while the inner race of the bearing 64 isclamped to the On the underside of the turntable are mounted six pairsof drive bars 72 (FIG. 4, section B-B). Into the slot formed by eachsuch pair of these drive bars 72 is slidably mounted a guide block 74which is rotatably connected to an output eccentric 76 integral with orbolted to a planetary gear 78. The distance from the center of eacheccentric 76 to the center of each planetary gear 78 may vary fromdesign to design from 0 to slightly more than the pitch radius of aplanetary gear 78. This is later referred to as R Each planetary gear 78is guided by two bearings 80 and 82 mounted in a planetary carrierassembly consisting of the lower ring plate 84, the upper ring plate 86,and six spacers 88. The lower ring plate 84 in turn is connected to thecase 60 through bearing 90 which guides the entire planetary carrierassembly 84, 86 and 88.

Each of the planetary gears 78 is suitably formed to mesh with astationary internal gear 92 which is rigidly bolted to the case 60. Itcan be seen, therefore, that when the planetary carrier assembly 84, 86and 88 is rotated about its bearing 90, by means described below, theplanetary gears 78 are caused to rotate about their individualcenterlines, as well as revolving within the internal gear 92. This inturn causes the output eccentrics 76 to drive the turntable 62 throughguide blocks 74 and drive bars 72. It will be further seen that themotion of the turntable 62 will be of an intermittent nature dependingon the eccentricity of the output eccentrics 76 relative to the pitchradius of the planetary gears 78.

An input eccentric 94 is bolted to or integral with each planetary gear78. Each input eccentric 94 is rotatably connected to a slide block 96which is slidably mounted in a slot 98 in the input driver ring 100(FIG. 4, section F-F). This input driver ring 100 i is supported fromthe case 60 through bearing 102 which is clamped to the case 60 by clampring 104 and clamped to the input driver ring 100 by clamp ring 106. Thedistance from the centerline of each input eccentric 94 to thecenterline of each planetary gear 78 may centricity of the inputeccentrics 94. Therefore, the

rotation of the driver ring 100 causes a rotation of the turntable 62,and the characteristics of the turntable 62 output movement aredependent on the eccentricities of both the input and output eccentricsrelative to the centers of the planetary gears.

In the drawings presented in FIGS. 3 and 4, the input and outputeccentrics are shown as lying in the same radial plane of each planetarygear. The output characteristics of the turntable may be furthercontrolled by introducing an angle between the radial plane thatcontains the input eccentric and the radial plane that contains theoutput eccentric. The effect of these quantities, input eccentricity,output eccentricity, and the phase angle between them, will be analyzedin the kinematic section below.

The input driver ring may be driven by any one of the systems of inputmeans described in connection with the input driver ring 50 shown inFIGS. 1 and 2.

Both mechanisms described above are comparable in three fundamentalrespects: in each case the output member is an open center turntable;the coupling system between the input member and the input eccentrics isthrough straight radial slots in the input member; and the couplingbetween the output member and the output eccentrics is also throughstraight radial slots created by bars on the output member. In themechanisms described below, two different examples of alternate designare presented.

Referring to FIGS. 5, 6, 7, 8, 9 and 10, the

mechanism is housed in a two-piece case and 112.

Suitable mounting feet or other attachment points may be appended tothis case as required. An input shaft 114 is mounted in suitablebearings 116 housed in case half 110. A seal 118 and bearing retainernut 120 of conventional design are applied as shown. An input spider122, FIG. 8, is welded or otherwise suitably attached to the input shaft114.

In the mechanism shown, four identical planetary gears are incorporated.It will be understood that this number is arbitrary and that the numberof planetary gear assemblies utilized in any given design may be variedwithin reasonable limits to meet the specific load requirements.

Each arm of the input spider 122 is pivot connected to an input link 124through a pin 126. The other end of each such input link 124 isconnected through bear ing 128 to an input eccentric 130 which isintegral with or bolted to a planetary gear 132.

The planetary gears 132 are mounted in bearings 134 and 136 which arehoused in a planetary carrier assembly which consists of a primary plate138, a secondary plate 140, and a spacer 142. This three-piece-assemblyis rigidly bolted or otherwise fastened into a single unit which issupported by hearing 144 mounted in the case half 110. l

The planetary gears 132 are suitably formed to mesh with a stationaryinternal gear 146 which is bolted between to case halves 110 and 112.The distance (dimension R later referenced) from the centerline of eachinput eccentric 130 to the centerline of each planetary gear 132 mayvary from design to design and may range in value from O to slightlyless than the pitch radius of a planetary gear 132.

It will be seen that as the input shaft is rotated (114), the inputspider 122 rotates with it. This in turn causes the input links 124 andinput eccentrics 130 to drive the planetary gears 132 and planetarycarrier assembly '138, 140, and 142, which rotates on its bearing 144,

while the planetary gears also rotate about their own axes in bearings134 and 136. It will be further seen that the rotation of the planetarycarrier assembly 138, 140 and 142 will be of a non-uniform naturerelative to the input spider 122, and that the degree of nonuniformityof rotation will be dependent upon the amount of eccentricity of theinput eccentrics 130 relative to the planetary gears 132. Thisnon-uniformity of rotation will also be dependent to a lesser degreeupon the lengths of the input links 124.

An output shaft 148 is suitably supported in bearings retainer nut 154are applied in a conventional manner as shown. An output spider 156(FIG. 7) is integral with or suitably rigidly fastened to the outputshaft 148; to each arm of this output spider 156 is attached an outputlink 158 through a pin 160. The other end of each output link 158 isconnected through a bearing 162 to an output eccentric 164 which isbolted to or integral with each planetary gear 132. The distance(dimension R later referred to) from the centerline of an outputeccentric 164 to the centerline of a planetary gear 132 on which it ismounted may vary from design to design and may range in value from toslightly more than the pitch radius of a planetary gear 132.

It will be seen that the rotation of the planetary carrier assembly 138,140 and 142 about bearing 144 and the rotation of the planetary gears132 about their own axes will cause a non-uniform rotation of the outputspider 156 and output shaft 148. It will be further seen that thisnon-uniformity of rotation of the output spider 156 and output shaft 148will be dependent upon the amount of eccentricity of the outputeccentrics 164 relative to their supporting planetary gears 132, and toa lesser degree dependent upon the lengths of the out put links 158.

Therefore, a rotation of the input shaft 114 causes a rotation of theoutput shaft 148 through the intermediate action of the input links 124,input eccentrics 130, planetary gears 132, output eccentrics 164, andoutput links 158. But for a given uniform rotation of the input shaft114, the rotation of the output shaft will be non-uniform, with thenon-uniformity dependent upon the input eccentricity, the outputeccentricity, and the lengths of both the input links 124 and the outputlinks 158.

In the mechanism shown in the drawings, FIGS. to 10, the input andoutputeccentrics were again shown as lying in the same radial plane of agiven planetary gear. It will be understood that this need not be thecase as has been described in connection with the prior examples.

In the mechanism presented in FIGS. 5 to 10, the coupling between theinput shaft and the planetary gears is through links; similarly, theconnection between the planetary gears and the output shaft is alsothrough links. This system is defined as the link mode as opposed to theslide mode illustrated in FIGS. 1 to 4. In some applications, it may beadvantageous to use a combination of these modes, i.e., a link modecoupling between the input shaft and the planetary gears in combinationwith a slide mode coupling between the planetary gears and the outputshaft, or vice versa. Such a system is defined as a hybrid system.

The mechanism shown in FIGS. 5 to utilizes a stationary internal gear tooperate with the planetary gears. An alternate version of a link modemechanism utilizing a stationary sun gear to operate the planetary gearsis shown in FIGS. 11 to 14. Referring to FIGS. 11 to 14, the mechanismis housed in a three-piece case consisting of frame 170, input bell 172,and output bell 174. An input shaft 176 is mounted in bearings 178housed in input bell 172; this assembly is retained in the input bell172 with bearing nut 180, and a seal 182 is mounted in a cover 184 alsobolted to the input bell 172.

The inner end of the input shaft 176 carries a pinion gear 186 suitablyformed to mesh with an input gear 188, mounted through bearings 190 to astationary shaft 192 which in turn is rigidly supported by the inputbell 172 and the output bell 174.

In the mechanism shown, four identical planetary gear assemblies areincorporated. It will be understood, as with previous mechanisms, thatthis number is arbitrary, and that the number of planetary gearassemblies utilized in any given design may be varied within reasonablelimits to meet the specified load requirements.

Four input spider arms 194, FIG. 12, are bolted to the inner face of theinput gear 188; an input-link 196 is pivot connected to each inputspider arm 194 through a pin 198. The other end of each input link 196is rotatably connected through bearing 200 to an input eccentric 202which is integral with or bolted to a planetary gear 204. The distance(dimension R later referenced) from the centerline of each inputeccentric 202 to the centerline of the planetary gear 204 on which it ismounted may again vary from design to design and may range in value fromO to slightly less than the pitch radius of a planetary gear 204.

The planetary gears 204 are mounted in bearings 206 and 208 which arehoused in a planetary carrier assembly which consists of a primary plate210, a secondary plate 212, and four spacers 214. This three-pieceassembly is rigidly bolted or otherwise fastened into a single unitwhich is supported by bearing 216 mounted on the stationary shaft 192.The planetary gears 204 are suitably formed to mesh with a stationarysun gear 217 which is rigidly mounted on the stationary shaft 192.

It will be seen that as the input gear 188 is rotated by the input shaft176, the spider arms 194, coupled to the planetary. gears 204 throughthe input links 196 and input eccentrics 202, cause the planetarycarrier assembly 210,212 and 214 to rotate about their own axes onbearings 206 and 208. It will be further seen that the rotation of theplanetary carrier assembly 210, 212 and 214 will be of a non-uniformnature relative to input gear 188, and that the degree of non-uniformityof rotation will be dependent upon the amount of eccentricity of theinput eccentrics 202 relative to the planetary gears 204. Thisnon-uniformity will also be dependent to a lesser degree upon thelengths of the input links An output ring gear 218 is mounted to thestationary shaft 192 through bearings 220. Four spider arms 222, FIG.14, are rigidly attached to one face of the output ring gear 218. Theoutboard ends of the spider arms 222 are pivot connected to the outputlinks 224 through pins 226. The other end of each output link 224 is inturn connected through a bearing 228 to an output eccentric 230 which isbolted to or integral with each planetary gear 204. As before, thedistance (dimension R later referenced) from the centerline of eachoutput eccentric 230 to the centerline of the planetary gear 204, onwhich it is mounted, may vary from design to design, and may range invalue from O to slightly more than the pitch radius of a planetary gear204.

The output ring gear 218 is suitably formed to mesh with the outputpinion 232 which is integral with or suitably fastened to the outputshaft 234, which in turn is mounted in bearings 236 housed in the outputbell 174. The output shaft assembly is retained by bearing nut 238 andsealed by seal 240 mounted in seal housing 242 which is bolted to theoutput bell 274.

It will be seen that the rotation of the planetary carrier assembly 210,212, 214 about bearing 216, and the rotation of the planetary gears 204about their own axes, will cause a non-uniform rotation of the outputring gear 218. It will be further seen that this nonuniformity ofrotation of the output ring 218 will be dependent upon the amount ofeccentricity of the output eccentrics 230 relative to their supportingplanetary gears 204, and to a lesser degree dependent upon the lengthsof the output links 224.

Therefore, a rotation of the input shaft 176 causes a non-uniformrotation of the'output shaft 234 through the intermediate action of theinput gear 188, input spider arms 194, input links 196, input eccentrics202, planetary gears 204, output eccentrics 230, output links 224,output spider arms 222, and output gear 218. The non-uniformity ofrotation of the output shaft 234 relative to the input shaft 176 is afunction of the input eccentricity, the output eccentricity, and thelengths of both the input links 196 and the output links 224.

In the mechanism shown in the drawings, FIGS. 11 to 14, the input andoutput eccentrics were again shown as lying in the same radial plane ofa given planetary gear. It will be understood that this need not be thecase as has been described in connection with the prior examples.

It will be noted that the mechanism of FIGS. 11 to 14 is a link modesystem as was the mechanism of FIGS. to 10. However, the mechanism ofFIGS. 11 to 14 utilizes a stationary sun gear operating with externalplanetary gears, as opposed to the mechanism of FIGS. 5 to whichutilizes a stationary internal gear operating with internal planetarygears.

In the four illustrative mechanisms shown, various combinations offeatures were employed. It will be understood that these combinationswere shown for purposes of example only, and other combinations may alsobe utilized, e.g., the direct shaft input may be utilized with a slidemode system, or 'a reduction shaft input may be combined with a tabletype output. The various features may be cross combined as required tomeet specific applications.

In addition, other important alternative designs, by

' way of example,are noted below.

system, the introduction of an internal gear, which meshes with allplanetary gears and therefore drives them with a constant speedreduction, with this internal gear either driven directly by the inputshaft, or driven through a reduction gear set; in the case of aninternal planetary system, the introduction of a sun gear which mesheswith all planetary gears and therefore drives them with a constant speedreduction, with this sun gear either directly driven by the input shaft,or driven through a reduction gear set.

In the slide mode systems as shown in the mechanisms of FIGS. 1 to 4,the slots in both the input and output members were shown as beingstraight and radial with respect to the axes of rotation of the inputand output members. Still greater kinematic flexibility can be achievedby making these slots straight and non radial, or curved with a constantor variable radius of curvature.

In the link mode systems as shown in the mechanism of FIGS. 5 to 14, thepivot connections between the input and output links and theirassociated spider arms were shown as lying on a line tangent to thelocus circle of the centers of the planetary gears at the point ofintersection with a radial line from the center of the planetary gearset, which contains both the center of a given planetary and the centerof the associated eccentric. This too may be changed .to achieve certainmechanical and kinematic objectives.

In order to make a qualitative analysis of the foregoing systems, thefollowing assumptions and definitions are presented:

1 It is assumed that the input shaft rotates at a constant angularvelocity.

2. The distance from the center of a given planetary gear to the centerof the input eccentric mounted thereon is defined as the input radius.

3. The distance from the center of a given planetary gear to the centerof the output eccentric mounted thereon is defined as the output radius.

The first analysis of a slide mode system, in which the slots arestraight and radial, will be made on the further assumption that theinput radius is zero, i.e., the input eccentrics are concentric withtheir respective planetary gears. Under these conditions, it will beseen that the planetary carrier assembly will rotate at the sameconstant speed as the input spider, and that the planetary gears willrotate on their own axes at a different constant speed dependent ontheir size relative to the stationary gear with which they are in mesh.

Under these conditions, and assuming that each output eccentric isdisplaced some distance from the centerline of its planetary gear, itcan be seen that:

When the output eccentrics lie between the centers of the planetarygears and the stationary gear with which they are in mesh (eitherinternal gear or sun gear) the output angular velocity is less than theinput angular velocity.

When the output eccentrics lie on the other side of the centers of theplanetary gears from the side on which they are in mesh, the outputangular velocity is greater than the input angular velocity.

The output velocity moves through one cycle for each revolution of aplanetary gear relative to its stationary mating gear, reaching amaximum or minimum when the center of the output eccentric, center ofthe planetary gear, and mesh point are in line; maximum when theplanetary center lies between the point of mesh and the center of theoutput eccentric, and minimum when the center of the output eccentriclies between the planetary gear center and the point of mesh. The outputvelocity changes smoothly between its maximum and minimum.

The amplitude of the difference between the maximum and minimumvelocities increases with increases in the output radius, until, whenthe output radius is made equal to the pitch radius of a planetary gear,a momentary stop is attained in the output velocity at the minimum pointwhen the center of the output eccentric is momentarily coincident withthe point of mesh. The corresponding maximum is less than twice theinput velocity in an external planetary system, and more than twice theinput velocity in an internal planetary system.

When the output radius becomes greater than the pitch radius of aplanetary gear, there is a reversal of the output velocity for a portionof the cycle. This is a useful property in lengthening the practicaldwell.

These foregoing characteristics apply strictly only to the slide modesystem with straight radial slots. It can be seen, however, that with alink mode system, the characteristics are generally the same, exceptthat the oscillation of the links adds a slight additional variation,which is dependent upon the link length and the location of the pivotconnection to the output spider.

When the input eccentrics are not concentric with the planetary gears,the velocity relationship between the input spider and the planetarycarrier is the exact reciprocal of the relationship described abovebetween the planetary carrier and the output spider. It should be notedthat if the input radius were to be made as large as the pitch radius ofthe planetary gear, a theoretically infinite velocity of the planetarycarrier would result. Therefore, the input radius must be kept slightlysmaller than the pitch radius of the planetary gears. This reciprocalrelationship is of great value in adjustmerit of the characteristics ofthe overall system.

The effects of the input and the output system are cumulative.Furthermore, since the input and output eccentrics may be radially andangularly displaced with respect to each other, an extraordinarily widevariation in output characteristics may be achieved through theknowledgeable choice of the three basic parameters: input radius, outputradius, and the phase angle between them.

The number of velocity cycles per revolution is determined by the ratioof the pitch diameter of the stationary gear to the pitch diameter ofthe planetary gears. In the case of external planetaries, there is notheoretical limit to this ratio. In the case of internal planetaries, adiscontinuity arises when the planetary pitch diameter is half theinternal gear pitch diameter and the output radius equals the pitchradius of the' planetary gear.

With reference to the kinematic development, several specific termsrequire definition. In the accepted sense, angular velocity means-therate of change of angular position with respect to time and will be soused in this disclosure; similarly, angular acceleration means the rateof change of angular velocity with respect to time and will be so usedin this disclosure.

In the mechanism described herein, the angular velocity and the angularacceleration characteristics of the output are dependent not only on themechanism but on the angular velocity and angular accelerationcharacteristics of the input. For most applications, the input will bemoved at a nominally constant angular velocity, except for the extremeends of the movement; therefore, the output angular velocity and angularacceleration characteristics will be calculated on the basis of anassumed constant angular velocity input. The term relative angularvelocity is defined for the purposes of this disclosure as the angularvelocity of the output assuming a constant input angular velocity; andthe term relative angular acceleration is defined for the purposes ofthis disclosure as the angular acceleration of the output again assuminga constant input angular velocity.

If the input does not move at a constant angular velocity, transferfunctions are stated which describe the output angular velocity as afunction of the input angular velocity, and other transfer functions arestated which describe the output angular acceleration as a function ofthe input angular velocity and input angular acceleration.

The output angular displacement characteristics relative to the inputangular displacement are, of course, unaffected by either the angularvelocity or angular acceleration of the input.

In the kinematic analysis which follows, the following symbols will beconsistently used and are defined as follows:

R Pitch radius of the planetary gear, which is taken as l for allanalyses unless otherwise noted.

p Pitch radius of the stationary gear; this is the sun gear in anexternal planetary system, and is the internal gear in an internalplanetary system.

R Radial distance from the center of the planetary gear to the center ofthe output eccentric.

R Radial distance from the center of the planetary gear to the center ofthe input eccentric.

d) Output angular displacement (of output spider) from its initialposition.

:11 Input angular displacement (of input spider) from its initialposition.

0 Angle through which the planetary gear has rotated from its initialposition. The initial position of the planetary gear is taken at thatpoint where the radial line between the center of the planetary gear andthe center of the stationary gear contains the center of the outputeccentric, and the center of the output eccentric is at its closestposition to the point of pitch line tangenu Phase angle between theplanetary gear radial line which contains the center of the inputeccentric and the planetary gear radial line which contains the centerof the output eccentric. It is defined as positive if the inputeccentric radial line is leading the output eccentric radial line in thedirection of planetary gear rotation.

V, True angular velocity of the output db/dl V Relative angular velocityof the output ddJ/dtll A, True angular acceleration of the output (1 ldtA Relative angular acceleration of the output z z In this and allsubsequent analyses, the angular displacement for both the input andoutput are most conveniently expressed in terms of 6, which becomes acalculating parameter. Expressing the output angle 11; directly in termsof the input angle ill is generally an extremely cumbersome procedure.Therefore, it is also far more convenient to differentiate with respectto 6 as required to obtain the solutions for relative angular velocityand relative angular acceleration. It can be shown for a general case,that if qb is some function of 0, 4) =f(), and ll} is some otherfunction of 0, r11 g(0), then d/dt1/and (fit/d4; can be expressed asderivatives with respect to 0 as follows:

These relationships will be used repeatedly and will be referred to asequation (1) and equation (2), as parenthetically noted.

It will be noted that the quantity dtlJ/dO appears in the denominator ofthe expressions for both V and A. Mathematically, this means that theexpressions become indeterminate at points where dull/d0 becomes zeroand such points must be avoided. Practically, this means that a point ofinfinite mechanical disadvantage arises for the input and the mechanismwill not move. Accordingly, such points will also be avoided.

Another valuable characteristic for investigation is the torque ratio ofthe output relative to the input, i.e., the units of output torquegenerated for each unit of input torque. Assuming a negligible frictionin the system, the torque ratio is the reciprocal of the relativeangular velocity. This is proven as follows:

Work in Work out T,- lnput Torque T Output Torque T dull T X d T /T,dill/d4) l/V All relative angular velocity graphs are therefore markedwith a second scale indicating the torque ratio of output to input.

Referring toFIG. 15, which is a kinematic line draw- .ing for aslide'mode external gear system; only the output system is shown, i.e.,the output angle is related to the planetary angle 6.

It can be seen that after the planetary gear has been rotated by theinput through an angle 0 from an initial starting position in which theradius R was colinear with the line' connecting the center of theplanetary gear with the center of the sun gear, the following angulardisplacement relationship exists:

These three equations, (3), (4), and (5) have to do with therelationships of the output angle (1) and the planetary angle 0. Toobtain the input-output relationship, the input system is now examined.

Referring to FIG. 16, which is a kinematic line drawing for a slide modeexternal gear system, showing the input system, which relates the inputangle \11 to the planetary angle 0. It will be noted that this isidentical 5 with FIG. 15, except for the terminology of the parameters.It can be seen that after the planetary gear has been rotated through anangle 6 from an initial starting position in which the radius R wascolinear with the line connecting the center of the planetary gear withthe center of the sun gear, the following angular displacementrelationship exists: if 0, 0 (1.1, 0):

R2 SiIIt i9 7 p+1R2cos0 (6) By differentiating this expression withrespect to 0, the following expression is obtained:

By differentiating again with respect to 0, the following expression isobtained:

l 2(p+ )l(p+ 2l sin! +R2 -2Rz(p+ (8) These three equations, (6), (7),and (8) have to do with the relationships of the input angle Ill and theplanetary angle 0. in this case where the planetary radii R and R arecolinear, and therefore the measure of 0 is the same for both the inputand the output conditions, the relative angular velocity of the outputis obtained by substituting equations (4) and (7) into equation (1 whichafter simplication results in the follow ing expression:

+1) +R 2R (p-l1) cos a (it p+1+R2 (p+2 2 s a (P+1)Z+RZ2' 2R2(P+1) e030(9 To obtain the expression for the relative angular acceleration,equations (4), (5), (7), and (8) may be substituted into equation (2),but the resultant algebraic expression becomes so cumbersome that it ismore convenient to accomplish the specific calculations by evaluatingeach derivative independently and then substituting their values intoequation (2) to obtain the relative angular acceleration. This techniqueis more acceptable because it is ordinarily desired to evaluate the 6derivatives independently in any case. For simplification of theseoperations, equation (2) may be rewritten:

E6 do Equation (3) expresses the output angular position; equation (6)expresses the input angular position; equation (9) expresses therelative angular velocity; and when equations (4), (5), (7), and (8) aresubstituted into equation (2) or (2a), the expression for the relativeangular acceleration is obtained. ln all cases 0 is a calculatingparameter. For every arbitrary value of 0, there can be calculated acorresponding value of (1), lb, ddJ/drll, and d tbldrlr Therefore, forevery valve Ill so obtained, there is a corresponding value of d),ddJ/dtll, and d /dllJ It is with these relationships that we areconcerned. in other words, 0 was used only as a mathematicalconvenience; and the output angular position, relative angular velocity,and relative angular acceleration will be shown in terms of the inputangular position, it.

Furthermore, since the input angular position change or angulardisplacement, for one acceleration cycle of the output, may vary interms of the absolute angle in degrees, the input angular displacementwill be expressed in terms of INPUT-FRACTIONOF CYCLE. A cycle is definedas one revolution of the planetary gear relative to the stationary gear,with the end points of the cycle defined as those points where theoutput radius R, is colinear with the line connecting the center of theplanetary gear and the center of the stationary gear, and the center ofthe output eccentric at its closest position to the point of geartangency. These generalizations apply to all subsequent analyses.

In this and all subsequent variations, only the relative angularvelocity curves will be presented, since these curves may be interpretedto indicate the angular displacement, and angular relative accelerationinformation in a comparative sense. It will be understood that the areaunder the relative angular velocity curve up to a given point is ameasure of the angular displacement up to that point, and that the slopeof the relative angular velocity curve at any point is a measure of therelative angular acceleration at that point. .ludicious andknowledgeable examination of the relative angular velocity curvesreveals both angular displacement and relative angular accelerationinformation.

In the special but important case where R, O, i.e., the eccentricity ofthe input eccentrics is 0, and the input eccentrics are concentric withthe axis of the planetary gears, the input spider and the planetarycarrier move in unison. In such cases the input spider and the inputeccentrics may be physically deleted and the planetary carrier drivendirectly, i.e., the planetary carrier becomes the input means. When R 0,equation (9) simplifies to the following:

p+1+ Rfi- (pl- R1 005 0 P+ l 1(P+ (5059 The relative angular velocitycurves resulting from i this equation (9a) for R, l, and for variousvalues of p are shown in FIG. 19. It will be remembered that this is forthe condition where the output spider has straight radial slots and thatthe planetary gears operate externally around a stationary sun gear,i.e., slide mode external planetaries. It will be noted that therelative angular velocity characteristics of the system are dependent onp, and while curves start and end at O and reach the axis with Zeroslope at each end of a cycle; their behavior is interestingly differentfor different values of p. For p =l, the relative angular velocityincreases rapidly at the beginning of the stroke, then levels off .cyclebecomes larger, until, as p approaches infinity,

the maximum relative angular velocity at mid-cycle approaches 2.

The relative angular velocity curves resulting from the more generalequation (9), whereby in R-fi 0, are

shown in FIG. 20. It will be understood that these curves are shown byway of illustration to indicate the effect of the parameter R for arepresentative fixed condition for the other parameters, in which p 4,and R, 1. It will be noted that the curve for R 0 in FIG. 20 isidentical with the curve in FIG. 19 in which p =4.

It will further be noted that for all values of R the curves aresymmetrical about the midpoint of the cycle, and that all curves stillreach the axis with zero slope at the ends of the cycle. As R is mademore positive, the relative angular velocity rises more rapidly from theends of the cycle, and becomes flatter during the center of the cycle,and reaches a lower peak value at mid-cycle. Conversely, if R is madeincreasingly negative, the opposite behavior of the relative angularvelocity curves is noted; i.e., the relative angular velocity increasesmore slowly from the ends of the cycle, but reaches a higher mid-cyclevalue, with a short duration of such higher value.

Therefore, while still maintaining symmetrical conditions about themidpoint of the cycle, a very high degree of versatility and control canbe obtained by judicious and knowledgeable choice of the R parameter.

These effects, while shown only for the single condition where p 4, andR, 1, apply also for other values of p, although it will be understoodthat the base curve, where R O, is different for each different value ofp.

' The foregoing represent the characteristics of a slide mode, in phase,external planetary system. To obtain the characteristics of a slidemode, out of phase, external planetary system, the following techniquesare used. Referring again to FIG. 16 and the equations derivedtherefrom, i.e., equations (6), (7), and (8), it can be seen that if 6,-in FIG. 16 is displaced from the 9 shown in FIG. 15, such that: l

where u is a constant angle defined as a phase angle between the radiusR, and the radius R such that it is positive if R, leads R, in thedirection of planetary gear rotation; then the relationships existingbetween i1; and 0 by successive differentiation become:

To obtain the relative angular velocity for the slide mode, out ofphase, external planetary system, equations (4) and (ll) are substitutedinto equation (I) which results in the following expression:

It should be noted that when R 0, equation (l3) becomes identical withequation (9a) which is as expected since u has no real meaning when R 0.

To obtain the value for the relative angular acceleration for thisout-of-phase condition, equations (4), (5 (ll), and (I2) may besubstituted into equation (2) or (2a), but the resultant algebraicexpression becomes socumbersome that it is more convenient to accomplishthe specific calculations by evaluating each derivative independentlyand then substituting their values into equation (2) or (20) to obtainthe relative angular acceleration. This technique is also more desirablebecause it is ordinarily desired to evaluate the 6 derivativesindependently in any case.

Curves representing the relationship expressed by equation (13) for therelative angular velocity for a slide mode, out of phase, external gearsystem are shown in FIG. 21. This set of curves is also presented by wayof example and illustration and is for the specific conditions where R,l, R 0.5, and p 4. Individual curves are plotted for phase angle valuesof u 30, 60, 90, 120, 150, and 180. It will be noted that the curve foru 0 is the same as the curve in FIG. 20 where R 0.50; and it will befurther noted that the curve for u 180 has the same geometric effect asnegative values of R at 0 phase angle.

The introduction of a phase angle produces a nonsymmetry in the relativeangular velocity curves (except for u 0 or u 180) which is clearlyevident in FIG. 21. This same general behavior or change incharacteristics is evident for other parameter combinations. It is alsoobvious that the general effect of the parameter u is more pronouncedfor larger values of R and is less pronounced for smaller values of Runtil, when R 0, u has no effect whatsoever.

These typical representative curves for the slide mode externalplanetary system are intended to illustrate the extremely wide kinematicrelationships which can be generated between the input and the outputthrough a knowledgeable and judicious choice of the various parameters.

For both mechanical and kinematic reasons, applications arise in whichit becomes desirable to utilize an internal rather than an externalplanetary system. The same analysis will now be made for a system inwhich the planetary gears operate with an internal stationary gear.

Referring to FIG. 17, which is a kinematic line drawing for a slide mode(straight radial slot) internal gear system; only the output system isshown, i.e., the output angle 4: is related to the planetary angle 0.

It can be seen that after the planetary gear has been rotated by theinput through an angle 6, from an initial starting position in which theradius R, was colinear with the line connecting the center of theplanetary gear to the center of the stationary gear, the followingangular displacement relationship exists:

6 R sin 0 tan p-1+ REE?) (14) By differentiating this expression withrespect to 0,

the following expression is obtained:

JG WT R1 HET W T By differentiating again with respect to 0, thefollowing expression is obtained:

These three equations (l4), (l5), and (16) have to do with therelationships of the output angle d) and the planetary gear angle 6. Toobtain the input-output relationship, the input system is now examined.

Referring to FIG. 18, which is a kinematic line drawing for a slide modeinternal gear system, showing the the input system which relates theinput angle ll: to the planetary gear angle 0. It will be noted thatthis is identical with FIG. 17 except for the terminology of theparameters. It can be seen that after the planetary gear has beenrotated through an angle 6 from an initial starting position in whichthe radius R was colinear with the line connecting the center of theplanetary gear with the center of the internal gear, and if 0, 0 (u 0),the following angular displacement relationship exists:

R; sine By differentiating this expression with respect to 0, thefollowing expression is obtained:

By differentiating again with respect to 6, the following expression isobtained:

, To obtain the expression for the relative angular aceeleration,equations l5), l6), I 8), and (19) may be substituted into equation (2)or (2a), but as inprior situations, it is more convenient to performthis operation in the implicit form.

Again as in the previous analyses, 0 is used as a calculating parameteras a mathematical convenience in establishing the desired relationshipsbetween the input displacement and the output displacement, relativeangular velocity and relative angular acceleration.

In the special but important case where R 0, i.e., the eccentricity ofthe input eccentrics is 0, and the input eccentrics are concentric withthe axes of the planetary gears, the input spider and the planetarycarrier move in unison. In such cases, the input spider and the inputeccentrics may be physically delected and the planetary carrier drivendirectly, i.e., the planetary carrier becomes the input means. When R 0,equation (20) simplifies to the following:

1R, ;2) R, cos 0 (p1) +R +2R (p1)COS 0 (20a) The relative angularvelocity curves resulting from this equation (20a) for R, l and forvarious values of p are shown in FIG. 22. It will be remembered thatthis is for the condition where the output spider has straight

1. A multiple step rotary indexing system having highly flexiblekinematic characteristics from input to output comprising: a. a firstsupport member, b. an input member rotatably mounted in said supportmember, c. an output member rotatably mounted in said support member andon the same axis as said input member, and d. an intermediate meansconnecting said input member to said output member comprising:
 1. astationary circular reaction member on the same axis as said inputmember and said output member,
 2. a planetary carrier frame rotatablymounted in said support member,
 3. one or more planetary members mountedin said planetary carrier frame positioned to roll without slipping onsaid circular reaction member in a planetary configuration,
 4. an inputshaft extending from each said planetary members, the axis of each saidshaft being parallel to, but displaced from, the axis of each saidplanetary member,
 5. means connecting said input member to each saidinput shaft,
 6. an output shaft extending from each said planetarymember, the axis of each said output shaft being parallel to the axis ofeach said planetary member, and
 7. means connecting said output memberto said output shaft.
 2. a planetary carrier frame rotatably mounted insaid support member,
 2. A multiple step rotary indexing system asdefined in claim 1 in which said circular reaction member is an externalgear having teeth to engage matching teeth on said plAnetary members. 2.input drive means connecting said input member and one side of saidplanetary gear member on axes of rotation spaced from the axis ofrotation of the gear members,
 3. output drive means connecting saidinput members and the other side of said planetary gear members on axesof rotation spaced from the axis of rotation of the gear members, and 3.A multiple step rotary indexing system as defined in claim 1 in whichsaid circular reaction member is an internal gear having teeth to engagematching teeth on said planetary members.
 3. one or more planetarymembers mounted in said planetary carrier frame positioned to rollwithout slipping on said circular reaction member in a planetaryconfiguration,
 4. an input shaft extending from each said planetarymembers, the axis of each said shaft being parallel to, but displacedfrom, the axis of each said planetary member,
 4. a means on said supportmember serving as a reaction gear track for engagement with externalteeth of said planetary gear members to transmit input motion to saidoutput member.
 4. A multiple step rotary indexing system as defined inclaim 1 in which the means connecting said input member to each saidinput shaft comprises a plurality of slide blocks slidably movable insaid input member in a predetermined guided path generally radial indirection from said input axis, and a rotary connection between saidrespective slide blocks and said respective input shafts.
 5. A multiplestep rotary indexing system as defined in claim 1 in which the meansconnecting said output member to each said output shaft comprises aplurality of slide blocks slidably movable in said output member in apredetermined guided path generally radial in direction from said outputaxis, and a rotary connection between said respective slide blocks andsaid respective output shafts.
 5. means connecting said input member toeach said input shaft,
 6. an output shaft extending from each saidplanetary member, the axis of each said output shaft being parallel tothe axis of each said planetary member, and
 6. A multiple step rotaryindexing system as defined in claim 1 in which the means connecting saidinput member to each said input shaft comprises a plurality of motiontransmitting links pivotally connected at spaced points respectively tosaid input member and to said input shafts of said planetary members. 7.A multiple step rotary indexing system as defined in claim 1 in whichthe means connecting said output member to each said output shaftcomprises a plurality of motion transmitting links pivotally connectedat spaced points respectively to said output member and to said outputshafts of said planetary members.
 7. means connecting said output memberto said output shaft.
 8. A multiple step rotary indexing system havinghighly flexible kinematic characteristics from input to outputcomprising: a. a support member, b. an input member and an output memberrotatably supported in axially spaced relation on said support member,c. means to drive said input member in rotation, and d. motiontransmitting means supported on said support means between said inputand said output members comprising:
 9. A multiple step rotary indexingsystem as defined in claim 8 in which said input and said output membersare each provided with slide tracks extending generally radiallythereof, and said input and output drive means include slide blocksmovable in said slots and rotatably associated with said planetary gearmembers.
 10. A multiple step rotary indexing system as defined in claim8 in which said input drive means includes a plurality of drive linksbetween said input member and said planetary gear members movable in aplane transverse of the axis of said input member each pivotedrespectively at spaced points to said input member and to a planetarygear member.
 11. A multiple step rotary indexing system as defined inclaim 8 in which said output drive means includes a plurality of drivelinks between said output member and said planetary gear members movablein a plane transverse of the axis of said output member, each pivotedrespectively at spaced points to said input member and to a planetarygear member.